The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of...
The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by E=35Z(Z-1)e24πε0R The measured masses of the neutron, H11, O158 are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u respectively. Given that the radii of both the N157 and O158 nuclei are same, 1u = 931.5 Me V/ c2 (c is the speed of light) and e2(4πϵ0)=1.44 MeV fm. Assuming that the difference between the binding energies of N157 and O158 is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm=10-15m)
Solution:
Electrostatic energy =BEN-BEO
=[[7MH+8Mn-MN]-[8MH+7Mn-MO]]×C2
=[-MH+Mn+MO-MN]C2
=[-1.007825+1.008665+15.003065-15.000109]×931.5
=+3.5359 MeV
∆E=35×1.44×8×7R-35×1.44×7×6R=3.5359
R=3×1.44×145×3.5359=3.42 fm
=[[7MH+8Mn-MN]-[8MH+7Mn-MO]]×C2
=[-MH+Mn+MO-MN]C2
=[-1.007825+1.008665+15.003065-15.000109]×931.5
=+3.5359 MeV
∆E=35×1.44×8×7R-35×1.44×7×6R=3.5359
R=3×1.44×145×3.5359=3.42 fm
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